Andrew Bennett, Nathan Kallus, Xiaojie Mao, Whitney Newey, Vasilis Syrgkanis, Masatoshi Uehara
arXiv 25 Jul 2023 · Statistics — Methodology · 1 citations (OpenAlex)
arXiv:2307.13793 · PDF · DOI · OpenAlex · Extracted main text
We consider estimation of parameters defined as linear functionals of solutions to linear inverse problems. Any such parameter admits a doubly robust representation that depends on the solution to a dual linear inverse problem, where the dual solution can be thought as a generalization of the inverse propensity function. We provide the first source condition double robust inference method that ensures asymptotic normality around the parameter of interest as long as either the primal or the dual inverse problem is sufficiently well-posed, without knowledge of which inverse problem is the more well-posed one. Our result is enabled by novel guarantees for iterated Tikhonov regularized adversarial estimators for linear inverse problems, over general hypothesis spaces, which are developments of independent interest.
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| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | N. Dikkala, G. Lewis, L. Mackey, and V. Syrgkanis (2020) Minimax estimation of conditional moment models | 1.000 | 9 | 5 | 100% |
| 2 | L. Liao, Y.-L. Chen, Z. Yang, B. Dai, M. Kolar, and Z. Wang (2020) Provably efficient neural estimation of structural equation models: An adversarial approach | 1.000 | 9 | 4 | 100% |
| 3 | A. Bennett, N. Kallus, X. Mao, W. Newey, V. Syrgkanis, and M. Uehara (2023) Minimax instrumental variable regression and $ l_2 $ convergence guarantees without identification or closedness | 1.000 | 7 | 3 | 100% |
| 4 | M. J. Wainwright (2019) High-dimensional statistics: A non-asymptotic viewpoint, volume 48 | 0.928 | 4 | 3 | 100% |
| 5 | A. Bennett, N. Kallus, X. Mao, W. Newey, V. Syrgkanis, and M. Uehara (2022) Inference on strongly identified functionals of weakly identified functions | 0.874 | 11 | 2 | 100% |
| 6 | L. Cavalier (2011) Inverse problems in statistics | 0.843 | 5 | 5 | 60% |
| 7 | V. Chernozhukov, D. Chetverikov, M. Demirer, E. Duflo, C. Hansen, an… (2017) Double/debiased/neyman machine learning of treatment effects | 0.843 | 3 | 3 | 100% |
| 8 | M. Carrasco, j.-p. Florens, and E. Renault (2007) Chapter 77 linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization | 0.737 | 3 | 2 | 100% |
| 9 | M. Carrasco, J.-P. Florens, and E. Renault (2007) Linear inverse problems in structural econometrics estimation based on spectral decomposition and regularization | 0.737 | 3 | 2 | 100% |
| 10 | Y. Cui, H. Pu, X. Shi, W. Miao, and E. T. Tchetgen (2020) Semiparametric proximal causal inference | 0.737 | 3 | 2 | 100% |
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